Show work TheCrazy Carmel Corn company has determined that the percentage of kernels that pop rises and then falls as the temperature of the oil the...

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The Crazy Carmel Corn company has determined that the percentage of kernels that pop rises and then falls as the temperature of the oil the kernels are cooked in increases. It modeled this trend using the equation:

P = -1/250t2+ 2.8t - 394

Where  P represents the percent of the kernels that pop and t represents the temperature of the oil in degrees Fahrenheit.

(a) Algebraically determine the temperature at which the highest percentage of kernels pop. Also, determine the percent of kernels that pop at this temperature.

(b) Using your calculator, sketch a curve below for P >/equal to 0 . Label your window.

(c) Using the ZERO command on your calculator, determine, to the nearest degree, the two temperatures at which P= 0 . Label them on your graph drawn in part (b).

(d) If a typical batch of popcorn consists of 800 kernels, how many does the Crazy Carmel Corn company expect to pop at the optimal temperature?

(e) For a batch of popcorn to be successful, the company wants at least 85% of its kernels to pop. Write inequality whose solution represents all temperatures that would ensure a successful batch. Solve this inequality graphically, to the nearest degree, and show your graph below, labeling all relevant points.